High school math will never be the same at Torrey Pines High School in San Diego, California. Abby Brown and her students are pushing the limits of traditional learning with Mathematica.
When Brown first began teaching, she used a single Mathematica license to quickly and accurately graph functions and typeset traditional math symbols for tests, quizzes, and handouts. A few years later, her school in conjunction with San Diego State University began a special program that gives advanced math students a chance to earn college credit in Calculus II, Multivariable Calculus, and Linear Algebra. To supplement these new courses, Brown used Mathematica to create visual aids such as graphs of tangential planes and matrix operation demos. She displayed the graphics during lectures with a projector attached to her computer. "Visualization is so valuable, and Mathematica is a tremendous tool for this," Brown explains.
Brown found even more ways to incorporate Mathematica into her lessons when her school purchased enough licenses to allow students to use it in math and science classes as well as in the central computer lab. "My philosophy focuses heavily on teaching using multiple methods of representation," says Brown. "My students' projects center on this, and Mathematica works well for combining graphical, symbolic, numerical, and verbal techniques."
Although Brown notes that she finds Mathematica most useful for teaching advanced courses, even her Algebra I students are captivated by the graphics and show improvement when she incorporates them into the course. One year, several Algebra I students didn't believe that the curve 1/x would never cross the x-axis. Using Mathematica, the students were able to investigate their theory by zooming in on the plot repeatedly, searching for an intersection. When they were satisfied that their teacher was correct, the students presented their final graphs to the class.
Using Mathematica is sometimes a challenge for Brown's students, but they are good at learning from their classmates' mistakes and helping each other with nuances of the code. The most common problems involve forgotten commas and capital letters. Brown has found that "with more practice, they learn to spot these errors and make fewer of them." Giving students early exposure to Mathematica will help them succeed in future math and science courses and can help increase their interest in technology-related fields.
Recently, Brown led several workshops to teach her colleagues how to take advantage of Mathematica as a teaching tool. She also wrote a tutorial titled "Exponentials vs. Factorials" to demonstrate how Mathematica can aid teaching in ways that aren't possible with a textbook or a graphing calculator.
Brown has also created a website that is a great resource for students and teachers. There is an activity section with puzzles, problems, and codes for students to solve. Ideas on how Mathematica can add a new dimension to math courses are available, and sample teaching modules in Mathematica notebook form can be downloaded. Brown has also included information on her teaching philosophy, sample student presentations, and links to other math-oriented web resources. View the site www.abbymath.com for more details.